It's possible that the switch does power an outlet, but that the installer did not remove the fin that connects the top and bottom outlets. When the fin is removed, the top and bottom outlets are isolated from one another so that they can be independently powered. If the top and bottom outlets are wired with two wires of the same phase, you would not notice a problem with day to day use.
If you have a voltage tester, test to see if you have power to both the top and bottom terminals of the switch when the switch is in the off position. If you do, it's likely the installer just forgot to take a fin off one or more of the outlets.
There is probably a way to test for this without any tools, but I am stuck at the moment. Maybe someone else will have a suggestion.
If you have reason to believe that the installer forgot to remove one or more duplex receptacle fins, you have to get in the outlet boxes to fix the problem. Take off the covers to the outlets in the room. If you're lucky, there will be both red and black wires connected to the receptacle(s) with switched power. These are the receptacles where the fin should be removed.
If there is only black wires and no red wires, your next step is to find out how the installer connected the outlets to one another another. He could have used pigtails, using wire nuts to connect the "line" (wires coming into the outlet box) to the "load" (wires going to the next outlet). Or he could have daisy chained the outlets together, meaning both the the line and the load load is connected directly to the receptacle. If you find that the installer used pigtails, you can just look for the receptacles where both the top and bottom outlets are wired. This receptacle likely has your switched outlet. If they are daisy chained, you have your work cut out for you. I can't think of any other way than to start taking apart the outlets and testing the wires one by one.
If you find a receptacle that needs the fin removed, and there is a shared neutral, only take the hot fin off. If there is a neutral for both outlets, then take both fins off.
Safety note: Don't assume that all the wires in one box are of the same circuit. Test ALL the wires in the box before you go in there with your hands.
You are describing a 3-way switch, which is among the most cheap and common electrical elements you will find.
You can pay up a bit for a 3-way switch with "pilot light" which will illuminate the switch when the circuit is closed (or open, depending on how wired), so that users will know whether toggling the switch will be turning the receptacle on or off.
Given the purpose you describe I would actually run the receptacle off of two single-pole switches wired in parallel so that it is on if either bathroom is calling for heat.
And yes, there are plenty of wireless solutions to toggle power at a wall receptacle if you want to spend the money for them instead of hard-wiring a 3-way switch.
Best Answer
I really question the wisdom of switching just the lower heating element. Doing so is going to overwork the upper element. I assume you are trying to conserve electricity, but this tactic is not going to be a great benefit to you. The upper element is used as the "quick recovery" unit that gives the cooling water from the lower part of the tank a boost as cold water is added as the hot water is used. If the water cools too much in the tank and you call for hot water, the upper element will not be able to keep up until the temp of the majority of the water warms up. I would suggest an inline switch or timer controlling both elements to help conserve energy and insulate the tank as much as you can. If you are looking for short, small quantities of hot water , you may consider a 1 or 2 gal point of use electric tank, in line at the specific appliance. There are several models to choose from at the box stores for under $300.00 I might add, if you do try this switch idea, you will need to switch both 120VAC lines with a DPST,(double pole, single throw) 30amp switch wired with 10AWG copper. When you open the thermostat cover, you will find the lines are connected to screw terminals on the thermostat switches.